Question

M is directly proportional to r^3
When r = 4, M= 160
b) work out the value of r when m = 540

Answer 1

Answer:

r=6

Step-by-step explanation:

Proportions

We know M is directly proportional to $r^3$

This can be written as

$M=kr^3$

Where k is the constant of proportionality which will be determined knowing that when r = 4, M= 160. Substituting in the equation above:

$160=k\cdot 4^3$

$160=k\cdot 64$

Solving for k:

$k=\frac{160}{64}=2.5$

The equation is:

$M=2.5\cdot r^3$

Now find r when M=540:

$540=2.5\cdot r^3$

Dividing by 2.5:

$216=r^3$

Taking cube roots:

$r=\sqrt[3]{216}$

r=6